Al-Hamadi broke the deadlock from a yard out to give Wimbledon a late first-half lead, before smashing the ball home after the break to seal the points at Plough Lane.
The Dons were forced to play the final 18 minutes a player short after Hus Biler picked up a second yellow card before Omar Bugiel was given his marching orders in stoppage time after also picking up two bookings but the hosts held on for all three points.
It was a cagey first half, with neither side able to test their opposition goalkeeper for much of the opening 45.
However, two minutes into first-half stoppage time, Al Hamadi was on hand to bundle home following a goal-mouth scramble to put the hosts in front.
The Iraq international bagged his second in the 63rd minute, pouncing on a slip from Rovers captain Tom Anderson before finishing into the top-right corner to secure their first league win in six for Wimbledon.